TNT equivalent

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Class of units of measurement for explosive energy

Ton of TNT
The explosion from a 14 kiloton nuclear test at the Nevada Test Site, in 1951.
General information
Unit system	Non-standard
Unit of	energy
Symbol	t or ton of TNT
Conversions
1 t in ...	... is equal to ...
SI base units	≈ 4.184 gigajoules
CGS	109 calories

TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. The ton of TNT is a unit of energy defined by that convention to be 4.184 gigajoules,^[1] which is the approximate energy released in the detonation of a metric ton (1,000 kilograms) of TNT. In other words, for each gram of TNT exploded, 4184 joules (or one large Calorie = 1,000 calories) of energy is released.

This convention intends to compare the destructiveness of an event with that of traditional explosive materials, of which TNT is a typical example, although other conventional explosives such as dynamite contain more energy.

Contents

• 1 Kiloton and megaton
• 2 Historical derivation of the value
• 3 Conversion to other units
• 4 Examples
• 5 Relative effectiveness factor
  • 5.1 Nuclear examples
• 6 See also
• 7 References

Kiloton and megaton[edit]

The "kiloton (of TNT)" is a unit of energy equal to 4.184 terajoules (4.184×10¹² J).

The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules (4.184×10¹⁵ J).

The kiloton and megaton of TNT have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon. The TNT equivalent appears in various nuclear weapon control treaties, and has been used to characterize the energy released in such other highly destructive events as an asteroid impact.^[2]

Historical derivation of the value[edit]

Alternative values for TNT equivalency can be calculated according to which property is being compared and when in the two detonation processes the values are measured.^[3][4][5][6]

Where for example the comparison is by energy yield, an explosive's energy is normally expressed for chemical purposes as the thermodynamic work produced by its detonation. For TNT this has been accurately measured as 4686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4853 J/g.^[7]

But, even on this basis, comparing the actual energy yields of a large nuclear device and an explosion of TNT can be slightly inaccurate. Small TNT explosions, especially in the open, don't tend to burn the carbon-particle and hydrocarbon products of the explosion. Gas-expansion and pressure-change effects tend to "freeze" the burn rapidly. A large open explosion of TNT may maintain fireball temperatures high enough so that some of those products do burn up with atmospheric oxygen.^[8]

Such differences can be substantial. For safety purposes a range as wide as 2673–6702 J has been stated for a gram of TNT upon explosion.^[9]

So, one can state that a nuclear bomb has a yield of 15 kt (6.3×10¹³ J); but an actual explosion of a 15000 ton pile of TNT may yield (for example) 8×10¹³ J due to additional carbon/hydrocarbon oxidation not present with small open-air charges.^[8]

These complications have been sidestepped by convention. The energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J,^[10] which is exactly one kilocalorie.

A kiloton of TNT can be visualized as a cube of TNT 8.46 metres (27.8 ft) on a side.

Grams TNT	Symbol	Tons TNT	Symbol	Energy [Joules]	Energy [Wh]	Corresponding mass loss
milligram of TNT	mg	nanoton of TNT	nt	4.184 J or 4.184 joules	1.162 mWh	46.55 fg
gram of TNT	g	microton of TNT	μt	4.184×103 J or 4.184 kilojoules	1.162 Wh	46.55 pg
kilogram of TNT	kg	milliton of TNT	mt	4.184×106 J or 4.184 megajoules	1.162 kWh	46.55 ng
megagram of TNT	Mg	ton of TNT	t	4.184×109 J or 4.184 gigajoules	1.162 MWh	46.55 μg
gigagram of TNT	Gg	kiloton of TNT	kt	4.184×1012 J or 4.184 terajoules	1.162 GWh	46.55 mg
teragram of TNT	Tg	megaton of TNT	Mt	4.184×1015 J or 4.184 petajoules	1.162 TWh	46.55 g
petagram of TNT	Pg	gigaton of TNT	Gt	4.184×1018 J or 4.184 exajoules	1.162 PWh	46.55 kg

Conversion to other units[edit]

1 ton TNT equivalent is approximately:

• 1.0×10⁹ calories
• 4.184×10⁹ joules
• 3.96831×10⁶ British thermal units
• 3.08802×10⁹ foot pounds
• 1.162×10³ kilowatt hours

Examples[edit]

Further information: Orders of magnitude (energy)

Megatons of TNT	Energy [Wh]	Description
1×10−12	1.162 Wh	≈ 1 food Calorie (large Calorie, kcal), which is the approximate amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius at a pressure of one atmosphere.
1×10−9	1.162 kWh	Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
1×10−8	11.62 kWh	The approximate radiant heat energy released during 3-phase, 600 V, 100 kA arcing fault in a 0.5 m × 0.5 m × 0.5 m (20 in × 20 in × 20 in) compartment within a 1-second period.[11][further explanation needed]
1.2×10−8	13.94 kWh	Amount of TNT used (12 kg) in Coptic church explosion in Cairo, Egypt on December 11, 2016 that left 25 dead[12]
(1–44)×10−6	1.16–51.14 MWh	Conventional bombs yield from less than one ton to FOAB's 44 tons. The yield of a Tomahawk cruise missile is equivalent to 500 kg of TNT, or approximately 0.5 tons.[13]
1.9×10−6	2.90 MWh	The television show MythBusters used 2.5 tons of ANFO to make "homemade" diamonds.
5×10−4	581 MWh	A real 0.5-kilotonne-of-TNT (2.1 TJ) charge at Operation Sailor Hat. If the charge were a full sphere, it would be 1 kilotonne of TNT (4.2 TJ). 500 tons of TNT (5 by 10 m (17 by 34 ft)) awaiting detonation at Operation Sailor Hat.
1.2×10−3	2.088 GWh	Estimated yield of the Beirut explosion of 2,750 tons of ammonium nitrate[14] that killed initially 137 at and near a Lebanese port at 6 p.m. local time Tuesday August 4, 2020.[15] An independent study by experts from the Blast and Impact Research Group at the University of Sheffield predicts the best estimate of the yield of Beirut explosion to be 0.5 kilotons of TNT and the reasonable bound estimate as 1.12 kilotons of TNT.[16]
(1–2)×10−3	1.16–2.32 GWh	Estimated yield of the Oppau explosion that killed more than 500 at a German fertilizer factory in 1921.
2.3×10−3	2.67 GWh	Amount of solar energy falling on 4,000 m2 (1 acre) of land in a year is 9.5 TJ (2,650 MWh) (an average over the Earth's surface).
2.9×10−3	3.49 GWh	The Halifax Explosion in 1917 was the accidental detonation of 200 tons of TNT and 2,300 tons of Picric acid
4×10−3	9.3 GWh	Minor Scale, a 1985 United States conventional explosion, using 4,744 tons of ANFO explosive to provide a scaled equivalent airblast of an eight kiloton (33.44 TJ) nuclear device,[17] is believed to be the largest planned detonation of conventional explosives in history.
(1.5–2)×10−2	17.4–23.2 GWh	The Little Boy atomic bomb dropped on Hiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 TJ) killing between 90,000 and 166,000 people,[18] and the Fat Man atomic bomb dropped on Nagasaki on August 9, 1945, exploded with an energy of about 20 kilotons of TNT (84 TJ) killing over 60,000.[18] The modern nuclear weapons in the United States arsenal range in yield from 0.3 kt (1.3 TJ) to 1.2 Mt (5.0 PJ) equivalent, for the B83 strategic bomb.
1	1.16 TWh	The energy contained in one megaton of TNT (4.2 PJ) is enough to power the average American household for 103,000 years.[19] The 30 Mt (130 PJ) estimated upper limit blast power of the Tunguska event could power the same average home for more than 3,100,000 years. The energy of that blast could power the entire United States for 3.27 days.[20]
4	4.6 TWh	The biggest H-bomb that China has detonated is 4 megatons of TNT
8.6	10 TWh	The energy released by a typical tropical cyclone in one minute, primarily from water condensation. Winds constitute 0.25% of that energy.[21]
21.5	25 TWh	The complete conversion of 1 kg of matter into pure energy would yield the theoretical maximum (E = mc2) of 89.8 petajoules, which is equivalent to 21.5 megatons of TNT. No such method of total conversion as combining 500 grams of matter with 500 grams of antimatter has yet been achieved. In the event of proton–antiproton annihilation, approximately 50% of the released energy will escape in the form of neutrinos, which are almost undetectable.[22] Electron–positron annihilation events emit their energy entirely as gamma rays.
24	28 TWh	Approximate total yield of the 1980 eruption of Mount St. Helens.
100	29–116 TWh	The Soviet Union developed a prototype weapon, nicknamed the Tsar Bomba, which was tested at 50 Mt (210 PJ), but had a maximum theoretical yield of 100 Mt (420 PJ).[23] The effective destructive potential of such a weapon varies greatly, depending on such conditions as the altitude at which it is detonated, the characteristics of the target, the terrain, and the physical landscape upon which it is detonated.
26.3	30.6 TWh	Megathrust earthquakes 2004 Indian Ocean earthquake released record ME surface rupture energy, or potential for damage at 26.3 megatons of TNT (110 PJ).
200	232 TWh	The total energy released by the 1883 eruption of Krakatoa in the Dutch East Indies (present-day Indonesia).
540	628 TWh	The total energy produced worldwide by all nuclear testing and combat combined, from the 1940s until the present is about 540 megatons.[citation needed]
1,460	1.69 PWh	The total global nuclear arsenal is about 15,000 nuclear warheads[24][25][26] with a destructive capacity of around 1460 megatons[27][28][29][30] or 1.460 gigatons (1,460 million tons) of TNT. This is the equivalent of 6.11x1021 joules of energy
33,000	38 PWh	The total energy released by the 1815 eruption of Mount Tambora in the island of Sumbawa in Indonesia.
104,400	121 PWh	The total solar irradience energy received by Earth in the upper atmosphere per hour.
875,000	1,000 PWh	Approximate yield of the last eruption of the Yellowstone supervolcano.
2.39×106	2,673 PWh	Approximate total yield of the super eruption of the La Garita Caldera was the second most energetic event to have occurred on Earth since the Cretaceous–Paleogene extinction event 65–66 million years ago. The asteroid impact responsible for that mass-extinction, equivalent to 100 teratons of TNT.
6×106	6,973 PWh	The estimated energy at impact when the largest fragment of Comet Shoemaker–Levy 9 struck Jupiter is equivalent to 6 million megatons (6 trillion tons) of TNT.
9.32×106	10,831 PWh	The energy released in the 2011 Tōhoku earthquake and tsunami was over 200,000 times the surface energy and was calculated by the USGS at 3.9×1022 joules,[31] slightly less than the 2004 Indian Ocean quake. This is equivalent to 9.32 teratons of TNT.
9.56×106	11,110 PWh	Megathrust earthquakes record huge MW values, or total energy released. The 2004 Indian Ocean earthquake released 9,560 gigatons TNT equivalent.
1×108	116,222 PWh	The approximate energy released when the Chicxulub impact caused the mass extinction 65–66 million years ago was estimated to be equal to 100 teratons (i.e. 100 exagrams or approximately 220.462 quadrillion pounds) of TNT (a teraton equals 1 million megatons). the most energetic event on the history of Earth for hundreds of millions of years, far more powerful than any volcanic eruption, earthquake or firestorm. Such an explosion annihilated everything within a thousand kilometres of the impact in a split second. Such energy is equivalent to that needed to power the whole Earth for several centuries.
3×108 - 119×108	349 EWh to 14 ZWh	Later estimates for the Chicxulub impactor energy have climbed to between 300 million megatons and 11,900 million megatons.[32]
5.972×1015	6.94×1027 Wh	The explosive energy of a quantity of TNT the mass of Earth.
7.89×1015	9.17×1027 Wh	Total solar output in all directions per day.
1.98×1021	2.3×1033 Wh	The explosive energy of a quantity of TNT the mass of the Sun.
(2.4–4.8)×1028	(2.8–5.6)×1040 Wh	A type 1a supernova explosion gives off 1–2×1044 joules of energy, which is about 2.4–4.8 hundred billion yottatons (24–48 octillion (2.4–4.8×1028) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (1012) times the mass of the planet Earth. This is the astrophysical standard candle used to determine galactic distances.
(2.4–4.8)×1030	(2.8–5.6)×1042 Wh	The largest type of supernova observed, gamma-ray bursts (GRBs) release more than 1046 joules of energy.[33]
1.3×1032	1.5×1044 Wh	A merger of two black holes, resulting in the first observation of gravitational waves, released 5.3×1047 joules

Relative effectiveness factor[edit]

The relative effectiveness factor (RE factor) relates an explosive's demolition power to that of TNT, in units of the TNT equivalent/kg (TNTe/kg). The RE factor is the relative mass of TNT to which an explosive is equivalent: The greater the RE, the more powerful the explosive.

This enables engineers to determine the proper masses of different explosives when applying blasting formulas developed specifically for TNT. For example, if a timber-cutting formula calls for a charge of 1 kg of TNT, then based on octanitrocubane's RE factor of 2.38, it would take only 1.0/2.38 (or 0.42) kg of it to do the same job. Using PETN, engineers would need 1.0/1.66 (or 0.60) kg to obtain the same effects as 1 kg of TNT. With ANFO or ammonium nitrate, they would require 1.0/0.74 (or 1.35) kg or 1.0/0.32 (or 3.125) kg, respectively.

Calculating a single RE factor for an explosive is, however, impossible. It depends on the specific case or use. Given a pair of explosives, one can produce 2× the shockwave output (this depends on the distance of measuring instruments) but the difference in direct metal cutting ability may be 4× higher for one type of metal and 7× higher for another type of metal. The relative differences between two explosives with shaped charges will be even greater. The table below should be taken as an example and not as a precise source of data.

Some relative effectiveness factor examples^{[citation needed]}

Explosive, grade	Density (g/ml)	Detonation vel. (m/s)	Relative effectiveness
Ammonium nitrate (AN + <0.5% H2O)	0.88	2700[34]	0.32[35][36]
Mercury(II) fulminate	4.42	4250	0.51[37]
Black powder (75% KNO3 + 19% C + 6% S, ancient explosives)	1.65	600	0.55[38]
Tanerit Simply (93% granulated AN + 6% red P + 1% C)	0.90	2750	0.55
Hexamine dinitrate (HDN)	1.30	5070	0.60
Dinitrobenzene (DNB)	1.50	6025	0.60
HMTD (hexamine peroxide)	0.88	4520	0.74
ANFO (94% AN + 6% fuel oil)	0.92	5270	0.74
TATP (acetone peroxide)	1.18	5300	0.80
Tovex Extra (AN water gel) commercial product	1.33	5690	0.80
Hydromite 600 (AN water emulsion) commercial product	1.24	5550	0.80
ANNMAL (66% AN + 25% NM + 5% Al + 3% C + 1% TETA)	1.16	5360	0.87
Amatol (50% TNT + 50% AN)	1.50	6290	0.91
Nitroguanidine	1.32	6750	0.95
Trinitrotoluene (TNT)	1.60	6900	1.00
Hexanitrostilbene (HNS)	1.70	7080	1.05
Nitrourea	1.45	6860	1.05
Tritonal (80% TNT + 20% aluminium)*	1.70	6650	1.05
Nickel hydrazine nitrate (NHN)	1.70	7000	1.05
Amatol (80% TNT + 20% AN)	1.55	6570	1.10
Nitrocellulose (13.5% N, NC; AKA guncotton)	1.40	6400	1.10
Nitromethane (NM)	1.13	6360	1.10
PBXW-126 (22% NTO, 20% RDX, 20% AP, 26% Al, 12% PU's system)*	1.80	6450	1.10
Diethylene glycol dinitrate (DEGDN)	1.38	6610	1.17
PBXIH-135 EB (42% HMX, 33% Al, 25% PCP-TMETN's system)*	1.81	7060	1.17
PBXN-109 (64% RDX, 20% Al, 16% HTPB's system)*	1.68	7450	1.17
Triaminotrinitrobenzene (TATB)	1.80	7550	1.17
Picric acid (TNP)	1.71	7350	1.17
Trinitrobenzene (TNB)	1.60	7300	1.20
Tetrytol (70% tetryl + 30% TNT)	1.60	7370	1.20
Dynamite, Nobel's (75% NG + 23% diatomite)	1.48	7200	1.25
Tetryl	1.71	7770	1.25
Torpex (aka HBX, 41% RDX + 40% TNT + 18% Al + 1% wax)*	1.80	7440	1.30
Composition B (63% RDX + 36% TNT + 1% wax)	1.72	7840	1.33
Composition C-3 (78% RDX)	1.60	7630	1.33
Composition C-4 (91% RDX)	1.59	8040	1.37
Pentolite (56% PETN + 44% TNT)	1.66	7520	1.33
Semtex 1A (76% PETN + 6% RDX)	1.55	7670	1.35
Hexal (76% RDX + 20% Al + 4% wax)*	1.79	7640	1.35
RISAL P (50% IPN + 28% RDX + 15% Al + 4% Mg + 1% Zr + 2% NC)*	1.39	5980	1.40
Hydrazine mononitrate	1.59	8500	1.42
Mixture: 24% nitrobenzene + 76% TNM	1.48	8060	1.50
Mixture: 30% nitrobenzene + 70% nitrogen tetroxide	1.39	8290	1.50
Nitroglycerin (NG)	1.59	7700	1.54
Methyl nitrate (MN)	1.21	7900	1.54
Octol (80% HMX + 19% TNT + 1% DNT)	1.83	8690	1.54
Nitrotriazolon (NTO)	1.87	8120	1.60
DADNE (1,1-diamino-2,2-dinitroethene, FOX-7)	1.77	8330	1.60
Gelignite (92% NG + 7% nitrocellulose)	1.60	7970	1.60
Plastics Gel® (in toothpaste tube: 45% PETN + 45% NG + 5% DEGDN + 4% NC)	1.51	7940	1.60
Composition A-5 (98% RDX + 2% stearic acid)	1.65	8470	1.60
Erythritol tetranitrate (ETN)	1.72	8206	1.60
Hexogen (RDX)	1.78	8700	1.60
PBXW-11 (96% HMX, 1% HyTemp, 3% DOA)	1.81	8720	1.60
Penthrite (PETN)	1.77	8400	1.66
Ethylene glycol dinitrate (EGDN)	1.49	8300	1.66
Trinitroazetidine (TNAZ)	1.85	8640	1.70
Octogen (HMX grade B)	1.86	9100	1.70
Hexanitrohexaazaisowurtzitane (HNIW; AKA CL-20)	1.97	9380	1.80
Hexanitrobenzene (HNB)	1.97	9400	1.85
MEDINA (Methylene dinitroamine)	1.65	8700	1.93
DDF (4,4'-Dinitro-3,3'-diazenofuroxan)	1.98	10000	1.95
Heptanitrocubane (HNC)	1.92	9200	N/A
Octanitrocubane (ONC)	1.95	10600	2.38

*: TBX (thermobaric explosives) or EBX (enhanced blast explosives), in a small, confined space, may have over twice the power of destruction. The total power of aluminized mixtures strictly depends on the condition of explosions.

Nuclear examples[edit]

Nuclear weapons and the most powerful non-nuclear weapon examples

Weapon	Total yield (kilotons of TNT)	Weight (kg)	Relative effectiveness
Bomb used in Oklahoma City (ANFO based on racing fuel)	0.0018	2,300	0.78
GBU-57 bomb (Massive Ordnance Penetrator, MOP)	0.0035	13,600	0.26
Grand Slam (Earthquake bomb, M110)	0.0065	9,900	0.66
BLU-82 (Daisy Cutter)	0.0075	6,800	1.10
MOAB (non-nuclear bomb, GBU-43)	0.011	9,800	1.13
FOAB (advanced thermobaric bomb, ATBIP)	0.044	9,100	4.83
W54, Mk-54 (Davy Crockett)	0.022	23	1,000
W54, B54 (SADM)	1.0	23	43,500
Hypothetical suitcase nuke	2.5	31	80,000
Fat Man (dropped on Nagasaki) A-bomb	20	4600	4,500
Classic (one-stage) fission A-bomb	22	420	50,000
W88 modern thermonuclear warhead (MIRV)	470	355	1,300,000
Typical (two-stage) nuclear bomb	500–1000	650–1120	900,000
W56 thermonuclear warhead	1,200	272–308	4,960,000
B53 nuclear bomb (two-stage)	9,000	4050	2,200,000
B41 nuclear bomb (three-stage)	25,000	4850	5,100,000
Tsar nuclear bomb (three-stage)	50,000–56,000	26,500	2,100,000

See also[edit]

• Brisance
• Net explosive quantity
• Nuclear weapon yield
• Orders of magnitude (energy)
• Relative effectiveness factor
• Table of explosive detonation velocities
• Ton
• Tonne
• Tonne of oil equivalent, a unit of energy almost exactly 10 tonnes of TNT

References[edit]

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